Past and future academic experiences are related with present scholastic achievement when intelligence is controlled

Learning and Individual Differences 32 (2014) 148–155

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Past and future academic experiences are related with present scholastic achievement when intelligence is controlled Gina C. Lemos a,⁎, Francisco J. Abad b, Leandro S. Almeida a, Roberto Colom b a b

Universidade do Minho, Portugal Universidad Autónoma de Madrid, Spain

a r t i c l e

i n f o

Article history: Received 17 May 2013 Received in revised form 7 January 2014 Accepted 24 January 2014 Keywords: Cognitive ability Academic achievement Academic failure Academic aspirations

a b s t r a c t Here the simultaneous relationships among cognitive ability (CA), past academic failure (PAF), future academic aspirations (FAA), and present scholastic achievement (PSA) were investigated. For addressing these rarely considered relations, two independent representative samples comprising 2796 students were analyzed; the first sample (young adolescents) included 1695 students from the third cycle of elementary school, whereas the second sample (old adolescents) comprised 1101 students from secondary school. SEM (structural equation model) analyses were computed and the main findings revealed that (1) CA, PAF, and FAA predict PSA, (2) CA is the best predictor of PSA, and (3) excluding PAF and FAA from the final SEM model produces a substantial reduction in the achieved predictive validity, especially for Language. © 2014 Elsevier Inc. All rights reserved.

1. Introduction Understanding the causes underlying the observed widespread differences in scholastic achievement is a basic goal of scientific research, and it is also relevant for society (Chen & Kaplan, 2003; Haveman & Smeeding, 2006; Heaven & Ciarrochi, 2012; Kao & Thompson, 2003; Lee, Hill, & Hawkins, 2012; Phillipson & Phillipson, 2012; Porter, 2002; Wilson, 2001). Pioneering research frameworks have nominated large sets of cognitive and non-cognitive relevant factors (Webb, 1915). In this regard, Harris (1940) and Cattell (1965) highlighted three basic domains: (i) cognitive ability, (ii) effort (drive or degree of motivation), and (iii) personal, economic, social, and academic circumstances. Cognitive ability is a well established predictor of scholastic achievement (Colom & Flores-Mendoza, 2007; Deary, Strand, Smith, & Fernandes, 2007; Jensen, 1998a; Laidra, Pillmann, & Allik, 2007; Neisser et al., 1996; Primi, Ferrão, & Almeida, 2010) with correlations ranging from .30 to .70 (Chamorro-Premuzic & Furnham, 2005; Deary et al., 2007; Jensen, 1998a,b; Kuncel, Hezlett, & Ones, 2004; Kyttälä & Lehto, 2008; Rosander, Bäckström, & Stenberg, 2011; Taub, Keith, Floyd, & Mcgrew, 2008), but non-cognitive factors also play a role (Bratko, Chamorro-Premuzic, & Saks, 2006; Conard, 2006; Farsides & Woodfield, 2003; Freiberger, Steinmayr, & Spinath, 2012; Furnham & Chamorro-Premuzic, 2004; Furnham, Chamorro-Premuzic, & McDougall, 2003; Gilles & Bailleux, 2001; Kane & Brand, 2006; Kappe & van der Flier, 2012; Noftle & Robins, 2007; O'Conner & Paunonen, 2007; Poropat, 2009). However, evidence

⁎ Corresponding author at: Centro de Investigação em Educação, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal. Tel.: +351 927433844. E-mail address: [email protected] (G.C. Lemos). 1041-6080/$ – see front matter © 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.lindif.2014.01.004

regarding further factors such as past academic failure and future academic aspirations is hardly considered. In this respect, Bandura (1986, 1997) suggested that academic aspirations (the desired scholar outcome or how much schooling is wanted) and expectations (the most likely scholar outcome pursued or how much schooling is expected) can be relevant predictors of present and future educational attainment and occupational status in adulthood (Beal & Crockett, 2010; Feliciano & Rumbaut, 2005; Kao & Thompson, 2003; MacLeod, 1995). It is generally accepted that a better previous academic background leads to better chances of success in present scholastic achievement. Recent research shows that educational aspirations are associated with actual achievement and are an important predictor of achievement in school and beyond (Rothon, Arephin, Klineberg, et al., 2011). Even after controlling for a number of variables, such as prior achievement, educational aspirations are still strongly related with students' achievement (Rothon et al., 2011). Academic aspirations and expectations are not stable throughout life and can be shaped and influenced, positively and negatively, by a wide constellation of factors (e.g. gender, age, ethnicity, sexual orientation, disability, socioeconomic status, religion, and other external factors such as peers, parents and teachers; e.g. Black, 2002; Cheng & Starks, 2002; Danziger & Eden, 2007; Goldstein, Davis-Keen, & Eccles, 2005; Mau & Bikos, 2000; Patton & Creed, 2007; Perry, Przybysz, & Al-Sheikh, 2009; Ryan, 2000). Further, these academic aspirations and expectations are particularly prone to changes over the course of adolescence (Beal & Crockett, 2010; Cooper, 2009; Eccles, Barber, Stone, & Hunt, 2003; Fredricks & Eccles, 2002). Cognitions about the future (e.g. school completion) take place during adolescence and become increasingly refined, more realistic, based on interests, perceived abilities, individual characteristics, and available opportunities (Crockett & Bingham, 2000; Eccles

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et al., 2003; Erikson, 1968; Nurmi, 2004). Adolescents' thoughts about their future might be important because they could influence outcomes such as choices, decisions, and activities, that may affect subsequent accomplishments and achievements (Beal & Crockett, 2010; Little, 2007; Nurmi, 2004). Moreover, both cognitive and non-cognitive factors contribute to the prediction of scholastic achievement with greater or smaller intensity depending on the considered educational stage (e.g., O'Conner & Paunonen, 2007). Thus, for instance, cognitive ability is usually less related with scholastic achievement at higher educational levels (Almeida, Guisande, Primi, & Lemos, 2008; Chamorro-Premuzic & Furnham, 2005; Laidra et al., 2007; Lemos et al., 2010), which can be explained by a number of reasons. The first is related to the restriction of ability range (Almeida et al., 2008; Boekaerts, 1995) meaning that students in higher levels of schooling are more alike regarding their general cognitive ability. A plausible argument to explain this homogeneity is that students with lower cognitive abilities choose alternative educational curricula usually not included in the regular samples of high school students, or contribute to early dropout. Another argument follows the “law of diminishing returns”. Originally proposed by Charles Spearman (1927), who reported that the average correlation between 12 cognitive ability tests was .466 in 78 normal children, and .782 in 22 “defective” children, this law (Spearman's Law of Diminishing Returns, SLDR) predicts that the g factor will account for a smaller proportion of individual differences in cognitive test scores at higher levels. The decreasing prediction of g at high educational levels may be due to smaller correlations among abilities in the more intelligent. These results were replicated elsewhere in a variety of children and adult samples (Deary & Pagliari, 1991; Detterman & Daniel, 1989; Tucker-Drob, 2009, but see Abad, Colom, Juan-Espinosa, & García, 2003). Secondly, the decreasing correlation between cognitive ability and scholastic achievement at higher educational levels can also be explained by the Gf–Gc investment theory (Cattell, 1971). This theory suggests a diminishing relevance of fluid intelligence (Gf) due to the emergence and development of crystallized intelligence (Gc), more involved with consolidated knowledge obtained by education, experience and interests throughout adolescence. The elementary school learning inputs can be understood as basic acquisitions, less centered in content than in form, strongly associated with the exercise of basic processes in perception, memory, and reasoning, and easily confounded with fluid intelligence (Gf). In learning inputs and scholastic achievement starting in adolescence, considering a curriculum which grows exponentially both in amplitude and complexity, knowledge and experience are requested to a greater extent — crystallized intelligence (Gc), or specific skills are predominant. Understanding Gf more like “inductive reasoning” and Gc as “acculturation knowledge” (Horn & Noll, 1997) fits this explanation that illustrates the progressive importance of knowledge, contents and domains of cognitive problems (Ackerman, 1996; Beauducel, Brocke, & Liepmann, 2001; Cattell, 1987; Gustafsson, 1984; Guttman & Levy, 1991; Schweizer & Koch, 2001). A third explanation is concerned with the increased contribution of further psychological factors associated with the learning process across school levels, such as educational aspirations and expectations, students' beliefs, motivation, study habits, students' approaches to learning, or vocational choices (Chamorro-Premuzic & Arteche, 2008; Eccles et al., 2003; Entwistle, Tait, & McCune, 2000; Fredricks & Eccles, 2002; Freiberger et al., 2012; O'Conner & Paunonen, 2007; Rosander & Bäckström, 2012; Steinmayr & Spinath, 2009). It is noteworthy that previous research has often neglected the analysis of the relation between cognitive ability and academic achievement taking into account variables such as past academic failure and future academic aspirations. For filling this gap, the present study comprehensively investigates the relationships among cognitive ability, past academic failure, future academic aspirations, and present scholastic achievement analyzing representative samples of students. To study the interplay of cognitive ability, past academic failure, future academic

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aspirations and scholastic achievement, two main models were tested: one that posits the exclusive relevance or direct effect of g, the named “only-g” model, and another model holding the relevance of further cognitive and other variables besides g, the named “non-only-g” model. Therefore, the present study tests if these two models are both suitable in predicting scholastic achievement on Language and Math, and, in particular, if both models have good fit indexes at the beginning and at the end of adolescence (young and old adolescents' samples, respectively). The potential contribution of specific cognitive skills is also addressed because, as noted above, they may differentially contribute to the prediction of different academic subjects (Bull & Johnston, 1997; Bull, Johnston, & Roy, 1999; Campos, Almeida, Ferreira, Martinez, & Ramalho, 2013; Geary, Hamson, & Hoard, 2000; Henry & MacLean, 2003; Kyttälä & Lehto, 2008; Rothstein, Paunonen, Rush, & King, 1994). 2. Method 2.1. Participants Two independent samples comprising 2796 students were considered. The first sample included 1695 students from the third cycle of elementary school (young adolescents; mean age = 13.5, SD = .97, range from 12 to 15 years) and the second sample comprised 1101 students from secondary school (old adolescents; mean age = 16.8, SD = .82, range from 16 to 19 years). All participants were involved in a larger study for the standardization of the Reasoning Test Battery (RTB; Almeida & Lemos, 2007) and answered some questions about past academic failure, future academic aspirations, and academic achievement. The samples were obtained randomly and state schools were selected considering previous stratification by regions in the country, school grade and gender within the class group at the school level. According to the annual school census of the Department of Assessment and Foresight and Planning – Ministry of Education – samples gather 6% of the Portuguese student population in the considered school levels. The school system in Portugal considers three cycles in elementary school and one cycle in secondary school. The present study takes students from the 3rd cycle of elementary school, equivalent to junior high school in other countries (7th–9th grades), and secondary school (10th–12th grades), when students choose from among several curricular options in order to follow different graduation areas in higher education or professional specialization. The first school level corresponds to the first sample mentioned above, whereas the second level matches the second sample. 2.2. Measures Intelligence was assessed through the Reasoning Tests Battery (RTB). The young adolescents performed the version designed for the first level (3rd cycle of elementary school) and the old adolescents performed the version designed for the second level (senior high school battery). In both cases, the RTB consists of five reasoning time-limited subtests: abstract reasoning (AR, 25 figural analogies and 5 min of administration time), numerical reasoning (NR, 20 numerical series and 10 min of administration time), verbal reasoning (VR, 25 verbal analogies and 4 min of administration time), mechanical reasoning (MR, 25 mechanical problem-solving items and 8 min of administration time), and spatial reasoning (SR, 20 spatial orientation and cube rotation series and 9 min of administration time). Fig. 1 shows examples of items from these subtests. Reliability indices were computed by test–retest and internal consistency methods. Obtained indices ranged from .63 (mechanical reasoning subtest) to .84 (numerical reasoning subtest). Factor analysis computed from different samples confirmed a single factor explaining between 50 and 60% of the variance (Almeida & Lemos, 2007). Previous confirmatory factor analysis confirms this general factor of intelligence (g) that predicts the five measures comprised in the battery in both

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Example of an Abstract Reasoning item

Example of a Numerical Reasoning item

Example of a Verbal Reasoning item

A. Marketer

4. Doctor is to patient as seller is to... B. Receipt C. Merchandise D. Customer E. Tradesman

Example of a Mechanical Reasoning item

Which pair of strings (A, B, C, D) actually prevents the advertising plaque from sagging? A. Strings 1 and 2 B. Strings 3 and 2 C. Strings 1 and 4 D. Strings 2 and 4 Example of a Spatial Reasoning item

Fig. 1. Example items from the administered intelligence battery.

samples (Lemos, Almeida, & Colom, 2011). A general score was computed summing the five reasoning standardized tests and this score was converted to the IQ scale (Mean = 100; SD = 15) for clarity purposes (see Colom et al., 2010). Past academic failure was measured by an item asking students to indicate whether they had ever failed a school year in their academic journey (1 = past failure, 0 = no failure). Future academic aspirations were measured by an item asking students to indicate how far in school they want to go: (1) until 9th grade or final of basic education (only applicable for young adolescents), (2) until 12th grade or final of secondary education, (3) to do a professional course, or (4) to do an academic higher education course. Present academic achievement was assessed by students' grades on Language (Portuguese) and Math.

2.3. Procedures A team of psychologists was trained for the administration of the intelligence battery by means of an 8 hour lasting training course. Before administration itself, strictly adhering to conditions specified in the battery's manual, participants were acquainted with the study's main aims as well as ethical concerns such as voluntary collaboration and data confidentiality. Then participants completed some brief questions about their past and present academic achievement and also about their future academic aspirations. Administration of the RTB and brief academic achievement questionnaire was completed by participants in classes with no more than 25 students during regular teaching hours, with the agreement of teachers. Schools' Executive Councils,

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and when necessary (students less than 16 years old) students' carers provided written informed consent. 2.4. Statistical analyses Several structural equation models were tested separately for the young and old adolescents, since some of the measures of interest were not exactly the same for both groups. First, the model depicted in Fig. 2 (excluding dotted arrows) was applied (“only-g” model). In this model, past academic failure and future academic aspirations predict present academic achievement in Math and Language. Furthermore, a general factor of intelligence (g) defined by the five cognitive measures [abstract reasoning (AR), numerical reasoning (NR), verbal reasoning (VR), mechanical reasoning (MR), and spatial reasoning (SR)] predicts directly past academic failure, future academic aspirations and present academic achievement. In the “only-g” model the specificity of each psychometric test does not predict Language and Math. In the “non-only-g” model, two theoretical plausible relationships are added (VR → Language and NR → Math). Model fit was assessed using the Root Mean Square Error of Approximation (RMSEA) and the Comparative Fit Index (CFI). Values close to .95 for CFI and below .06 for RMSEA suggest a good fit (Hu & Bentler, 1999). The Akaike Information Criteria (AIC; Akaike, 1987) and the Bayesian Information Criterion (BIC; Raftery, 1995) were also used for comparing models. AIC and BIC are sensitive to model parsimony. When comparing models, the smaller these indices the better the fit. All models were fitted using maximum likelihood with Mplus (Muthen & Muthen, 2012). Percentile-based bias-corrected bootstrap Confidence Intervals were obtained to test indirect effects (Hayes, 2009; Zhao, Lynch, & Chen, 2010). Equality of standardized regression weights was tested by creating new parameters with the NEW option in Mplus (Cheung, 2009). 3. Results The descriptive statistics along with the correlation matrix are shown in Table 1. Note that past academic failure was .20 for both young and old adolescents indicating that 80% of students tend to succeed in both junior high school and secondary school. The mean scores for future academic aspirations (young adolescents, 3.5 and old adolescents, 3.8) showed

Fig. 2. The “only-g” model (excluding dashed lines) and the “non-only-g model” (including all paths). Residual variances for predicted variables are not represented.

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that students from junior high school and secondary school want to follow a post-secondary professional course or an academic higher education course. Regarding the correlations among the study variables, it can be seen that numerical reasoning is correlated with Math (young adolescents r = .37; old adolescents r = .31) and verbal reasoning is correlated with Language (young adolescents r = .37; old adolescents r = .33). Correlations between cognitive ability and academic achievement slightly decrease for the old adolescents (e.g., IQ score correlations with Math were .40 and .33 for the young and the old adolescents, respectively). Correlations between past academic failure and future academic aspirations decrease for the old adolescents (young adolescents, −.40 and old adolescents, −.28). Math and Language show a high correlation for both samples (around .60). In the next step, structural equation models were tested. Fit indices are reported in Table 2. Afterwards, we computed multiple regression models (Language and Math on g, past failure and future aspirations) for the young and old adolescents. For both the groups, this model showed a good fit (CFI N .95; RMSEA around 0.06). For the young adolescents, standardized weights were significant for Language (g: .28; future aspirations: .19; past failure: −.15) and Math (g: .36; future aspirations: .18; past failure: − .13) explaining 22% of Language performance and 27% of Math performance. Correlations among predictors were significant (g correlated .32 and −.33 with future aspirations and past failure, respectively; future aspirations and past failure correlated − .40). For the old adolescents, standardized weights were significant on Language (g: .22; future aspirations: .18; past failure: − .22) and Math (g: .31; future aspirations: .14; past failure: −.12) explaining 19% of Language performance and 17% of Math performance. Correlations among predictors were significant (g correlated .23 and −.26 with future aspirations and past failure, respectively; future aspirations and past failure correlated −.28). With respect to the mediation models (only-g and non-only-g) these were the main results for both groups. Regarding the young adolescents, both mediation models showed a good fit (CFI N .95; RMSEA around .06), but the “only-g” model showed a worse fit than the “non-only-g” model. The final non-only-g model is depicted in Fig. 3a. According to the bootstrap confidence intervals, all the tested indirect (mediation) effects were significant (p b 0.01) and all the standardized factor loadings and regression weights were significant (p b .01). Standardized regression weights of past failure (B = − .33) and future aspirations (B = .32) on g were equal in size (p N .05). Regression weights of Language (B = .19, −.14, .11) and Math (B = .18, −.14, .26) were equal on aspirations (p N .05), on past fail (p N 0.5) but not on g (p b .01). All the predictors (g, VR, NR, past failure, and aspirations) explained 22% of Language and 26% of Math. Excluding past failure and future aspirations reduced the percentage of explained variance to 15%, for Language, and 20%, for Math. Of the total effects of g on Language, 31% were direct, 39% were mediated by VR, and the remaining mediated by aspirations (17%) and past failure (13%). Of the total effects of g on Math, 59% were direct, 18% were mediated by NR, and the remaining mediated by aspirations (13%) or past failure (10%). For the old adolescents, both models showed a good fit, but the “non-only g” model fitted better. The final non-only g model is depicted in Fig. 3b. All the tested indirect (mediation) effects were significant with p b 0.01 or p b .05 (g → NR → Math) and all the standardized factor loadings and regression weights were significant with p b .01 or p b .05 (NR → Math). Standardized regression weights of past failure (B = − .26) and future aspirations (B = .23) on g were equal in size (p N .05). Regression weights of Language (B = .18, .14, − .22) and Math (B = .15, .23, −.12) were equal on aspirations (p N .05) and g (p N .05) but not on past failure (p b .01). All the predictors (g, VR, NR, past failure, and aspirations) explained 20% of Language and 17% of Math. Excluding past failure and future aspirations reduced the percentage of explained variance to 11% for Language, and to 13% for Math. Of the total effects of g on Language, 46% were direct, 22% were

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Table 1 Descriptive statistics and correlation coefficients of both samples. AR

NR

VR

MR

SR

Fail

Aspir

Lang

Math

IQ

– .46 .47 .37 .43 −.22 .19 .21 .27 .75

.38 – .45 .38 .47 −.22 .24 .26 .37 .75

.29 .33 – .40 .40 −.30 .28 .37 .32 .74

.32 .40 .31 – .36 −.07 .08 .15 .19 .69

.49 .50 .33 .44 – −.21 .20 .24 .30 .73

−.16 −.19 −.17 −.11 −.19 – −.40 −.31 −.32 −.28

.17 .12 .16 .10 .17 −.28 – .34 .35 .27

.13 .25 .33 .15 .19 −.33 .29 − .58 .34

.19 .31 .32 .14 .23 −.24 .24 .60 – .40

.70 .73 .64 .70 .78 −.23 .21 .30 .33 –

Young adolescents (N = 1695) Mean 12.7 SD 3.2

8.6 3.7

14 3.7

9.3 3.2

9.6 4

0.2 0.4

3.5 0.8

3.1 0.7

3.1 0.9

100 15

Old adolescents (N = 1101) Mean 12.1 SD 2.8

9.6 3.6

15.6 3.3

9.7 3.5

10.4 3.5

0.2 0.4

3.8 0.5

12.5 2.8

12 3.5

100 15

AR NR VR MR SR Failure Aspirations Language Math IQ

Note. Correlations below the diagonal are for young adolescents. Correlations above the diagonal are for old adolescents.

mediated by VR, 13% were mediated by future aspirations and 19% were mediated by past failure. Of the total effects of g on Math, 65% were direct, 17% were mediated by NR, 9% were mediated by future aspirations and 9% were mediated by past failure. Finally, because the administered tests differed across age groups, measurement invariance tests were not applicable. Nevertheless, the equality of within-group standardized loadings and regression weights across age groups was tested using a multi-group model. The model is depicted in Fig. 3c. Results showed that standardized regression weights were remarkably similar for both groups, with minor exceptions: (a) aspirations on g (.31 vs .24; p b .05), (b) Language on past failure (−.14 vs − .23, p b .05), (c) AR on g (.66 vs .50; p b .01), (d) VR on g (.67 vs .55; p b .01) and (e) SR on g (.64 vs .75; p b .01). In summary, the reported analyses support the perspective that previous academic failure and future academic aspirations contribute to the prediction of scholastic achievement. The variance explained considering all the significant predictors was: (a) for the young adolescents 26% (Math) and 22% (Language) and (b) for the old adolescents 17% (Math) and 20% (Language). The percentage of explained variance was reduced to 4–9%, when excluding past failures and future aspirations. 4. Discussion Here we have shown that cognitive ability differences, past academic failure and future academic aspirations are related with present academic achievement. These simultaneous relationships are generally invariant across the age groups considered. Beyond this general conclusion, there are several noteworthy points that can be derived from the reported results. First, general cognitive ability is a direct predictor of scholastic achievement for the young and old adolescents. This result can be

Table 2 Fit indices for the young and old adolescents. X2

df

RMSEA

CFI

SRMR

AIC

BIC

Young adolescents “Only-g”a 173.1 “Non-only g” 103.3

21 19

0.065 0.051

0.961 0.979

0.033 0.028

55875.6 55809.8

56055.0 56000.0

Old adolescents “Only-g”a 116.0 “Non-only g” 86.6

21 19

0.064 0.057

0.956 0.969

0.039 0.033

40862.0 40836.6

41027.1 41011.7

Note. a Fit equivalent to the multiple regression model.

framed within R. B. Cattell's investment theory (Cattell, 1987). This theory suggests that abstract or fluid reasoning evolves to knowledgebased problem solving (crystallized ability) throughout the developmental process. As adolescents get older, specific abilities grounded on education, experience, and interests may overcome fluid intelligence. An increased specialization/differentiation of cognitive abilities is expected as individuals aged and pass through cultural exposure and the educational curricula (Schweizer & Koch, 2001). This is not particularly consistent with the findings observed here because a greater relevance of verbal and numerical reasoning for the old adolescents is expected with respect to their Language and Math academic achievement. Secondly, past academic failure and future academic aspirations are predicted by general cognitive ability (g) with values ranging from .24 (old adolescents) to .31 (young adolescents). Therefore, the higher the general ability (a) the greater the future academic aspirations and (b) the lower the likelihood of having experienced past academic failure. Table 1 showed direct correlations between future academic aspirations and present scholastic achievement (between .24 and .35) as well as between the latter and past academic failure (between − .24 and −.33). These values are reduced when general cognitive ability is considered as a covariate (see Fig. 3a, b, and c) but they are still statistically significant. Thus, the predictive validity of past academic failure and future academic aspirations should not be minimized. Excluding these variables from the prediction model reduced several points the percentage of explained variance (Language and Math) for the young and old groups. Third, the relationships among many of the variables of interest are generally invariant across age (Chamorro-Premuzic & Furnham, 2005; Eccles et al., 2003; Laidra et al., 2007; O'Conner & Paunonen, 2007; Rosander & Bäckström, 2012; Steinmayr & Spinath, 2009): (a) general cognitive ability predicts past academic failure with a value of − .30, (b) general cognitive ability predicts future academic aspirations with values of .31 and .24 for the young and old adolescents respectively, and (c) general cognitive ability is directly related with academic achievement in the young and old adolescents (.14 for Language and .25 for Math), (d) verbal reasoning and numerical reasoning are also predictors of Language (.17) and Math (.10) respectively, and (e) abstract reasoning, spatial reasoning, and mechanical reasoning are unrelated with present academic achievement, as measured by Language and Math, mainly because their relevant variance is captured by g for the young and old adolescents. In summary, here we have shown that the analysis of representative samples of students highlights the multivariate nature of academic achievement. Individual differences in the learning outcomes involved in Language and Math academic subjects are predicted by cognitive

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Fig. 3. (a) Model for the young adolescents (N = 1695), (b) model for the old adolescents (N = 1101), and (c) multi-group model. For non-invariant parameters, values between parentheses are for the old adolescents.

abilities, past academic failure, and future academic aspirations. Students with higher cognitive scores, less academic previous failures and greater future academic aspirations do better in school, as measured by their performance in Language and Math. Improving the latter is openly relevant for society, as persistently claimed by international research such as PISA. It is true that academic achievement is multivariate in nature, but the relevant variables must be hierarchically organized for a proper understanding of the involved factors. Previous academic failure and future academic aspirations considered in the present study are relevant, but nonetheless they are less important than cognitive abilities. Thus, improving students' academic performance must begin with the close analysis of how their individual differences in these

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